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Nonlinear Dynamics

, Volume 57, Issue 4, pp 497–507 | Cite as

Analytical bifurcation analysis of a rotor supported by floating ring bearings

  • A. Boyaci
  • H. Hetzler
  • W. Seemann
  • C. Proppe
  • J. Wauer
Original Paper

Abstract

Like with other types of fluid bearings, rotors supported by floating ring bearings may become unstable with increasing speed of rotation due to self-excited vibrations. In order to study the effects of the nonlinear bearing forces, within this contribution a perfectly balanced symmetric rotor is considered which is supported by two identical floating ring bearings. Here, the bearing forces are modeled by applying the short bearing theory for both fluid films. A linear stability analysis about the static equilibrium position of the rotor shows that for a critical revolution speed the real part of an eigenvalue pair changes its sign. By means of a center manifold reduction it is shown that this destabilization of the steady state is due to a Hopf-bifurcation. Furthermore, the type of this bifurcation is determined as well as the existence and stability of limit-cycles. Notably it is found that depending on the parameters of the floating ring bearing subcritical as well as supercritical bifurcations may occur. Additionally, the analytical results obtained from the center manifold reduction are compared to numerical results by a continuation method. In conclusion, the influences of bearing design parameters on the stability and on the limit-cycles are discussed.

Keywords

Stability Hopf-bifurcation Center manifold reduction Floating ring bearing Rotor dynamics Analytical investigation Numerical continuation 

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References

  1. 1.
    Doedel, E.J.: AUTO-07P: Continuation and bifurcation software for ordinary differential equations. Concordia University, Montreal (2006) Google Scholar
  2. 2.
    Guckenheimer, J., Holmes, Ph.: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer, New York (1983) MATHGoogle Scholar
  3. 3.
    Hollis, P., Taylor, D.L.: Hopf bifurcation to limit cycles in fluid film bearings. ASME J. Tribol. 108, 184–189 (1986) CrossRefGoogle Scholar
  4. 4.
    Holt, C., San Andrès, L., Sahay, S., Tang, P., La Rue, G., Gjika, K.: Test response and nonlinear analysis of a turbocharger supported on floating ring bearings. ASME J. Vib. Acoust. 127, 107–115 (2005) CrossRefGoogle Scholar
  5. 5.
    Lang, O.R., Steinhilper, W.: Gleitlager. Springer, Berlin (1978) Google Scholar
  6. 6.
    Li, C.H.: Dynamics of rotor bearing systems supported by floating ring bearings. ASME J. Lubr. Technol. 104, 469–477 (1982) Google Scholar
  7. 7.
    Moser, F.: Stabilität und Verzweigungsverhalten eines nichtlinearen Rotor-Lager-Systems. Dissertation, TU Wien (1993) Google Scholar
  8. 8.
    Muszynska, A.: Rotordynamics. CRC Press, Boca Raton (2005) MATHGoogle Scholar
  9. 9.
    Myers, C.J.: Bifurcation theory applied to oil whirl in plain cylindrical journal bearings. ASME J. Appl. Mech. 51, 244–250 (1984) MATHCrossRefGoogle Scholar
  10. 10.
    Tanaka, M., Hori, Y.: Stability characteristics of floating bush bearings. J. Lubr. Technol. 93(3), 248–259 (1972) Google Scholar
  11. 11.
    Tondl, A.: Some Problems of Rotor Dynamics. Chapman & Hall, London (1965) Google Scholar
  12. 12.
    Troger, H., Steindl, A.: Nonlinear Stability and Bifurcation Theory. Springer, New York (1991) MATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • A. Boyaci
    • 1
  • H. Hetzler
    • 1
  • W. Seemann
    • 1
  • C. Proppe
    • 1
  • J. Wauer
    • 1
  1. 1.Institut für Technische MechanikUniversität KarlsruheKarlsruheGermany

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